An ex-racehorse, fresh off the track, of any breed (SB, QH, TB, etc.) would not be suitable for any beginner.
You have two issues with off the track horses: genetics and training.
horses breeding counts. If a horse comes from a bloodline that is a "racing" line then all of the genetic selection for racing will be there. This is the material that a trainer will have to work with. Just how it manifests itself in any given horse can vary some, but the variability is narrower than some folks (particularly from the "off the track rescue community") would have you believe.
After a period of seasoning and retraining an ex-racer might
prove suitable for a beginner. But all ex-racehorses are, always, ex-racehorses. It's been my obervation that the "race training" can, and will, resurface from time to time as it was very intense and is very deep-seated in the horse's memory. If the quality of "remedial" training is good and the base temperment is good and the rider is capable of handling "flashbacks" then you're OK. But if not...???
Personally, I'd never put a greenie on an ex-racer. I just don't want to take that much risk. There are so many good, quiet horses without the genetic and training baggage I don't see the need to even approach the risk. As the rider skill increases then we can talk about horses with higher levels of potentially risky equine behavior.